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A063841 Table T(n,k) giving number of k-multigraphs on n nodes (n >= 1, k >= 0) read by antidiagonals. 7
1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 10, 11, 1, 1, 5, 20, 66, 34, 1, 1, 6, 35, 276, 792, 156, 1, 1, 7, 56, 900, 10688, 25506, 1044, 1, 1, 8, 84, 2451, 90005, 1601952, 2302938, 12346, 1, 1, 9, 120, 5831, 533358, 43571400, 892341888, 591901884, 274668, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The first five rows admit the g.f. 1/(1-x), 1/(1-x)^2, 1/(1-x)^4 and those given in A063842, A063843. Is it known that the n-th row admits a rational g.f. with denominator (1-x)^A000124(n)? - M. F. Hasler, Jan 19 2012

LINKS

Table of n, a(n) for n=1..55.

Harald Fripertinger, The cycle type of the induced action on 2-subsets

Vladeta Jovovic, Formulae for the number T(n,k) of n-multigraphs on k nodes

EXAMPLE

Table begins

1 1 1 1 ...

1 2 3 4 ...

1 4 10 20 ...

1 11 66 276 ...

T(3,2)=10 because there are 10 unlabelled graphs with 3 nodes with at most 2 edges connecting any pair.

(. . .),(.-. .),(.-.-.),(.-.-.-),(.=. .),(.=.=.),(.=.=.=),(.-.=.),(.-.-.=),(.=.=.-) -Geoffrey Critzer, Jan 23 2012.

MATHEMATICA

(* This code gives the array T(n, k). *) Needs["Combinatorica`"]; Transpose[Table[Table[PairGroupIndex[SymmetricGroup[n], s]/.Table[s[i]->k+1, {i, 0, Binomial[n, 2]}], {n, 1, 7}], {k, 0, 6}]]//Grid (* Geoffrey Critzer, Jan 23 2012 *)

CROSSREFS

Columns give A000088, A004102, A053400, A053420, A053421.

Rows (4th and 5th) are listed in A063842, A063843.

Sequence in context: A122175 A073165 A137153 * A256161 A137596 A111669

Adjacent sequences:  A063838 A063839 A063840 * A063842 A063843 A063844

KEYWORD

nonn,nice,tabl

AUTHOR

N. J. A. Sloane, Aug 25 2001

EXTENSIONS

More terms from Vladeta Jovovic, Sep 03 2001

STATUS

approved

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Last modified May 29 01:07 EDT 2017. Contains 287241 sequences.